Calculate the probability of being in the excited state

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Quantum statistical mechanics: Another two-level system
Although a two-level system might seem very simple, it is very important and occurs frequently in various guises. Here is another form that we will see often. A system only has two states, which are both non-degenerate. The energies of these two states are E = 0 and E = ? > 0. The system is in contact with a heat reservoir at temperature T.

1. Calculate the probability of being in the excited state.

2. Calculate the average energy. Sketch it as a function of temperature.

3. Calculate the average specific heat. Sketch it as a function of temperature.

4. Calculate the two leading terms in a high-temperature expansion of the energy in powers of β = 1/k_BT.

5. Calculate the leading (non-constant) term in a low-temperature power series expansion of the energy in some variable at low temperatures. (Hint: the variable will be in the form of an exponential.)

Reference no: EM131347975

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